The rookies got the news before practice on Monday from head coach Michel Therrien, who told them they were staying with the NHL club and that they should move out of their hotel and find somewhere to live.
The 18-year-old Galchenyuk said he would stay with his mother and sister, while Gallagher is moving in with veteran defenceman Josh Gorges and his fiancee.
Therrien was pleased with those arrangements.
"For (general manager) Marc Bergevin and me, it's really important that our young players are looked after on the ice and it's crucial they are looked after away from the ice," he said. "Alex living with his family is excellent for us because we don't want to leave a young player alone in a city like Montreal where there are a lot of distractions.
"It's the same for Gallagher. Even if he's 20, it's his first season as a pro and we also want him well supported."
Galchenyuk, 18, drafted third overall in June from the junior Sarnia Sting, has a goal and two assists and is plus-2 in four NHL games.
Gallagher, a fifth round pick in 2010 who started his first pro season with Hamilton of the AHL this season, scored his first NHL goal Sunday against New Jersey. He has two points and is also plus-2.
They have looked sharp playing together on the team's third line with veteran Brandon Prust.
"As the week went on, the more we saw the way it was going," said Therrien. "We were convinced they were ready to play at this level.
"We also considered their maturity level. Because of their work habits, these young players have earned the respect of their teammates. They have bought into the team concept. The bottom line is they deserved to stay."
The Canadiens are 3-1-0.
Veteran defenceman Andrei Markov, who has scored in three consecutive games, was given the day off practice after posting 29:50 of ice time in a 4-3 win Sunday night over New Jersey, when he notched the game-winner in overtime.
Therrien confirmed that Carey Price will start a fifth straight game on Tuesday night against the visiting Winnipeg Jets.
He said back-up Peter Budaj will start one of the three other games this week — either Wednesday in Ottawa, Saturday at home against Buffalo or Sunday afternoon when the Senators visit.